Elementary math formulas

Quick reference for elementary school. Browse by topic or search by name.

Addition & subtraction

Commutative property of addition

a+b=b+aa + b = b + a
Changing the order of addends does not change the sum.
Addition & subtraction

Associative property of addition

(a+b)+c=a+(b+c)(a + b) + c = a + (b + c)
Addition & subtraction

Additive identity

a+0=aa + 0 = a
Addition & subtraction

Checking addition

a+b=c  ⇒  c−a=ba + b = c \;\Rightarrow\; c - a = b
If the sum is correct, c − a equals the second addend.
Addition & subtraction

Subtraction as addition

a−b=a+(−b)a - b = a + (-b)
Multiplication

Commutative property of multiplication

a⋅b=b⋅aa \cdot b = b \cdot a
Multiplication

Distributive property

a⋅(b+c)=a⋅b+a⋅ca \cdot (b + c) = a \cdot b + a \cdot c
Multiply each addend, then add the products.
Multiplication

Multiplication by zero

a⋅0=0a \cdot 0 = 0
Multiplication

Multiplication by one

a⋅1=aa \cdot 1 = a
Division

Meaning of division

a÷b=c  ⇔  a=c⋅b(b≠0)a \div b = c \;\Leftrightarrow\; a = c \cdot b \quad (b \neq 0)
Division

Division by one

a÷1=aa \div 1 = a
Division

A number divided by itself

a÷a=1(a≠0)a \div a = 1 \quad (a \neq 0)
Division

Division by zero

a÷0a \div 0
Division by zero is undefined.
Order of operations

Operation priority

( )  →  ×(\,) \;\rightarrow\; \times
÷  →  +\div \;\rightarrow\; +
−-
Parentheses first, then × and ÷ left to right, then + and −.
Fractions

Fraction as part of a whole

ab\frac{a}{b}
The fraction \frac{a}{b} means a parts out of b equal parts.
Fractions

Adding fractions with the same denominator

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}
Fractions

Subtracting fractions with the same denominator

ac−bc=a−bc\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}
Fractions

Comparing fractions with the same denominator

ac>bc  ⇔  a>b\frac{a}{c} > \frac{b}{c} \;\Leftrightarrow\; a > b
Fractions

Fraction of a number

n⋅abn \cdot \frac{a}{b}
To find \frac{a}{b} of n, multiply n by the fraction.
Units of measure

Length

1 km=1000 m1\,\text{km} = 1000\,\text{m}
1 m=100 cm1\,\text{m} = 100\,\text{cm}
1 cm=10 mm1\,\text{cm} = 10\,\text{mm}
Units of measure

Mass

1 kg=1000 g1\,\text{kg} = 1000\,\text{g}
Units of measure

Time

1 h=60 min1\,\text{h} = 60\,\text{min}
1 min=60 s1\,\text{min} = 60\,\text{s}
Units of measure

Area

1 m2=10 000 cm21\,\text{m}^2 = 10\,000\,\text{cm}^2
1 are=100 m21\,\text{are} = 100\,\text{m}^2
1 ha=100 are1\,\text{ha} = 100\,\text{are}
Geometry

Rectangle perimeter

P=2(a+b)P = 2(a + b)
a and b are side lengths.
Geometry

Rectangle area

S=a⋅bS = a \cdot b
Geometry

Square perimeter

P=4aP = 4a
Geometry

Square area

S=a2S = a^2
Geometry

Triangle area

S=a⋅h2S = \frac{a \cdot h}{2}
a is the base, h is the height to that base.
Percents

What is a percent

1%=11001\% = \frac{1}{100}
Percents

Percent of a number

n⋅p100n \cdot \frac{p}{100}
To find p\% of n, multiply n by \frac{p}{100}.
Percents

Percent as a fraction

p%=p100p\% = \frac{p}{100}